A wild finish to the baseball season

Never say never

IN A memorable scene from the 1994 film “Dumb and Dumber”, Jim Carrey's character asks his love interest to assess the probability of their becoming a couple. “Not good”, she responds. “Not good, like, one out of a hundred?”, he presses her, seeking statistical precision. “I'd say more like one out of a million,” comes the reply. Mr Carrey then concludes jubilantly: “So you're telling me there's a chance. Yeah!” Such logic may indeed be dumb when applied to romance. However, after what may well have been the most improbable confluence of events to occur in a professional sport within a single day in history, it seems an entirely apt description of baseball.

Let's turn back the clock a few weeks. On September 3rd the Boston Red Sox had a won-lost record of 84-54, while the team behind them, the Tampa Bay Rays, was at 75-63. According to the calculations at coolstandings.com, that gave Boston a 99.6% chance of making the postseason tournament. Five days later, the Atlanta Braves' record was 84-60, while that of their rivals, the St Louis Cardinals, was 76-67. Atlanta was then 98.4% likely to advance to the playoffs.

Both Boston and Atlanta promptly fell into epic slumps. The Red Sox lost 17 of their next 23 games, and the Braves 12 of their next 17. Meanwhile, Tampa Bay and St Louis heated up, and tied their struggling competitors on the season's penultimate day. If either the Red Sox or Braves failed to hold off their challengers, their collapses would rank among the most precipitous in history—right there with that of the 1951 Brooklyn Dodgers, whose defeat was chronicled in Don DeLillo's novel “Underworld”.

St Louis won its last game of the year. That meant the Braves would need to best the formidable Philadelphia Phillies just to stay tied. They were poised to do just that as they entered the final inning with a one-run lead, giving them an 87% chance of victory. But in the most important appearance of his career, Craig Kimbrel, Atlanta's dominant relief pitcher, suddenly lost his ability to throw the ball in the vicinity of home plate. He allowed three walks and one run, sending the game into extra innings. Four frames later, the Phillies scratched home a run and the Braves could not match it. This graph of the probability of an Atlanta victory throughout the game is a powerful representation of their path to defeat.

About one hour later, the Red Sox found themselves in an identical position. They too were clinging to a one-run lead going into the ninth inning and had a star relief pitcher, Jonathan Papelbon, headed to the mound. Mr Papelbon struck out the first two batters he faced, making Boston 95% likely to win. But one batter away from victory, Boston's 86-year curse seemed to re-emerge. The next two batters doubled, tying the game. Then Carl Crawford—the left fielder whom Boston signed away from Tampa Bay last winter for $142m, in part because of his defensive prowess—misplayed the next hitter's line drive, allowing the winning run to score. If you thought the Braves' graph was heartbreaking, take a look at this one.

Yet neither of those turnarounds could compare to the evening's you-have-got-to-be-kidding-me capstone. To end Boston's season without facing them in a one-game playoff, the Rays would have to beat the New York Yankees. In the eighth inning of that contest, Tampa Bay was down 7-0—putting their probability of victory at one in 333.

But as Mr Carrey would have it, there was still a chance. The Rays rallied for six runs, leaving them down by just one going into the final frame. The Yankees did not score. In the ninth inning, the first two Rays struck out. In desperation they summoned Dan Johnson—by one measure the worst batter in baseball this year—as a pinch-hitter. Mr Johnson quickly went down two strikes. With just one pitch separating the Rays from defeat, he crushed the next offering into the seats for a game-tying home run. Three extra frames later, Evan Longoria hit a walk-off home run to send the Red Sox—who presumably were watching the game on television—home. Yeah—here's the graph.

Let's rehash. There was something on the order of an 0.5% chance the Red Sox would blow their nine-game lead over the Rays, and a 2% chance the Braves would lose their seven-and-a-half-game edge over the Cardinals. Then in tonight's matchups, there was a 13% chance the Phillies would come back to beat Atlanta, a 5% chance the Orioles would come back to beat Boston, and an 0.3% chance the Rays would come back to beat New York. Multiply it all out, and the odds of witnessing what we just witnessed were worse than one in 500m. Suddenly, Mr Carrey's optimism seems entirely justifiable.

Leaving aside all this drama—recounted in a minute-by-minute timeline at ESPN—baseball's overlords may not be pleased with the outcome. Nothing generates more ticket revenues and television ratings than a Yankees-Red Sox playoff series, which has not occurred since 2004. And despite the Rays' appeal as an underdog, they are a 13-year-old franchise in a tiny market. The only World Series they have appeared in (2008) got the lowest television ratings for a Fall Classic in a generation.

Nonetheless, even if Tampa Bay's comeback will cost Major League Baseball money in the short run, the club's success has positive ripple effects. Sports leagues need their big-market teams to win more than their fair share of the time, but not so often as to remove all suspense about the outcome. The presence of franchises with no hope whatsoever hurts every club—even rich ones, whose fans may not want to pay to see their squad obliterate an overmatched rival. The fact that the Rays have made the playoffs three times in four years gives the lie to the moans of other small-market teams that they cannot afford to compete. Tampa Bay's victory is a win for fans in Pittsburgh, Kansas City and San Diego as well.

ADDENDUM: A number of commenters at Baseball Think Factory have noted that the probability of any single permutation of events out of nearly infinite possibilities is infinitesimally small, but one of those highly unlikely combinations will always have to come to fruition. Millions of one-in-500m events take place every day. As one user writes, “In the last week, Craig Gentry hit an inside-the-park home run as his first major-league homer, while the Rays pulled off a round-the-horn triple play and the Diamondbacks came back from a five-run deficit with two out in their last inning. Multiply that by the chance that the White Sox would trade their manager to Florida and that I would rent the Lon Chaney version of The Hunchback of Notre Dame out of the hundreds of thousands of DVDs in print, and basically last week couldn't have happened even before you add in last night.”

This is a valid point. It would have been equally amazing had the Yankees squandered their division lead instead of the Red Sox, or if the Orioles rather than Rays had come back from seven runs down in the eighth inning. I did not count those possibilities in my calculation, which would have reduced the odds from 500m:1 to something marginally smaller. To get a “fairer” idea of the probabilities, however, we have to define the set of events whose likelihood we're trying to calculate. If it's not “Boston and Atlanta blow their division leads, Baltimore and Philadelphia come back from a run down in the ninth, and Tampa Bay rallies from seven down in the eighth,” what is it? The odds that at least two teams would blow leads of at least seven and a half games, and that at least three teams involved in the playoff chase would stage comebacks from win probabilities below 15% on the last day of the season? That's still a narrow set of criteria, and a rather lame attempt to generalise from the specific combination of events we saw last night.

I'm not sure how you'd devise a list of requirements to calculate a probability without referring one way or another to the exact path of yesterday's games. But I would challenge readers to come up with any chapter of athletic history that was even less likely than baseball's 2011 regular-season finale. I'll be watching the comment threads.

This was a fascinating night for baseball. Almost poetically, the rainout in Baltimore gives the O's / Red Sox the chance to watch the Rays come back, and then the rain delay lifts and the games end almost in sync with walkoffs. The only way to describe this series of events: "the odds of witnessing what we just witnessed were worse than one in 500m"

1. Picking baseball talent & developing talent - notably pitchers - makes up for money. If that were easy, more teams would be better at it. But then again, it may be runs of luck, just outcomes happening because they happen. Some team will develop a bunch of good players and people will think they have the "gift" and then that gift seems to move to another club. It may be as simple as one or two good drafts and those may depend on the talent available that year and that talent not getting hurt.

2. We still can't quantify choking or coming through under pressure. That's true for individuals and for teams. I've seen work on this, even some arguing it doesn't exist.

3. Great addition to Red Sox lore. This is the kind of thing Boston fans really need: a good kick to the groin to remind them of suffering. Boston isn't really a front running town. And now there's so much to pick at: John Lackey's performance (the worst pitcher in the history of the team), the front office's failure, the inability to come from behind from the 7th inning on, the great season Papelbon had but then failure (again) when it really counted, why a team with so much payroll has so many flaws, etc. All that goes away when you win. Complaining, worrying, wondering is the spice of life.

Your calculations are somewhat flawed; those probabilities are not independent. You would need to subtract a certain amount of covariance from each of those calculations to get the real probability, which may or may not turn out to be significantly different. In any case, what an amazin turnaround!

This was by far the best day of regular season baseball of all time. It almost seemed like a twilight zone having the rays come back from a 7-0 deficit and having the red sox lose a 3-2 lead. Not to mention this happened in a span of four minutes.

This was astonishing to watch. The Redsox blow it and the Rays overcome the terrible yanks to clinch the AL Wild Card. Ridiculous. One night to go down in the books. Redsox blew a lead on the Rays in the last month. They had it...and choked. From Pedroia to Big Papi, they have many clutch players, who this year couldn't find the right gear in the end to win the race. I would have thought, the yankees being the yankees, they would have given the game to the Rays just so Boston would need to win their game and the one game playoff with the rays. Boston needs a good offseason to rethink the 2011 season because of their historic choke. Both teams knew what was on the line. It was who came up to play who goes through. The Rays won their game with a fight, while Boston...ha we all know what happened there. nothing. no one did anything. They fell apart. Better to get them out of the way and have a team that comes to play when it matters in the playoffs than a team like boston who has been on a downfall since August.

For example, it could be that a team playing badly (as evidenced by its recent record) is more likely to blow a big lead. Let's say conditional on losing a nine game advantage, the likelihood of a team winning it's next game falls by 10% (due to the team not playing well, injury, fatigue, what have you). Then it becomes more likely that this team having a lead in the next game in the first place is simply good fortune, and that some mean reverting process will cause the team to "blow it". Certainly seems possible; I'm not saying it's a huge deal but it could be. I think it's worth investigating.

I am not exactly out in the street with my "Save Francona" T-shirt, but it's Theo Epstein who has to go. The guy has wasted a lot of $ on big ticket players who have failed to deliver and robbed the Sox of the former 'scrappiness'. Basically made them boring.

This epic collapse is going to bring a lot of changes to Boston. Terry Francona's job as a baseball manager doesn't require much x and o strategy. His job as a manger is to manage his player and inspire them to play. Losing a nine game lead in September is unacceptable as a manager and a leader. Red Sox nation has to be out for Francona's head.

Wow. Usually I like to comment on article's of global significance that impact millions of people. For example, earthquakes in Pakistan or arguments in the Middle East. However, this article was amazing! The odds of witnessing those sports accomplishments yesterday was almost 1 to infinite. Its glad to get our minds away sometimes from global problems.

I've never read through any article about baseball - ever - until tonight. Almost makes me wish i'd watched the games - which, BTW, is high praise. Having attended a few baseball games with colleagues it always seems so utterly silly, nearly to the point of sadness, watching these adult men vicariously live out their prepubescent fantasy of running around under bright lights in silly polyester costumes while everyone cheers them on (and that this fantasy, of all available, is the one they would choose) but if Mr Carey's character can get the girl (I assume he did; I've never seem a Jim Carey movie either - probably some correlation there) then I suppose it summons the false feeling that all is possible - which is a lovely escape.

If last night was any indication of the playoffs this year, I think we're all in for a treat. It goes to show that any team can beat any other on any given day. Nobody is safe, and that's what makes sports so great.

Baseball has always been the best thing to teach people about how wildly improbably things, things so improbably as to be functionally impossible, do happen.

I am of course referring to the video of Randy Johnson nailing a pigeon with a fastball. The odds of a pigeon flying doen at just the right time were incredibly low, couple that with the odds of flying down in front of not just any pitcher, but arguably the best in baseball at the time, you wouldn't believe it if wasn't on camera.

This is one of those nights people will talk about for years (if they're baseball fans, of course.) The odds of this kind of thing happening to the Red Sox and Braves in one September is unimaginable, especially for the Sox after spending so much money this offseason (warranted or not). Besides both teams going into a spiral, and the Devil Rays and Cardinals showing how much heart they have, as a baseball fan, it is just unbelievable. What hasn't been made enough of though is the fact that all that money the Red Sox spent really hasn't improved their teams, and all three guys (Lackey, Crawford and Gonzalez) all seem to never be able to play at the level that "warranted" the huge contracts, with Gonzalez playing the best (but still overpaid, in my opinion). Overall though, amazing baseball night.

UR8S6bVvVa: Why wouldn't they be independent? The events are the likelihood that two teams in different leagues would blow their leads before the last day of the year, and the likelihood of comebacks in three subsequent games played simultaneously in different cities. I don't see any covariance...